Calculate commission percentage by amount

Question

In our system, we got a booking of the price 1100, the default commission percentage is 15% hence the raw price is

1100 / 1.15 = 956.52173913

Which means that the current commission amount is

1100 - 956.52173913 = 143.47826087

I need to change the commission percentage of this booking, but i only know the commission amount which is 100

How do i calculate the new commission, based on the only on commission amount?

Answer 1

More general. The following formula can be solved for $x$.

$P\cdot \left(1-\frac{1}{1+x}\right)=C$

with $P=$ gross price, $x$=comission rate and $C$=commission

Multipying out the brackets

$P-\frac{P}{1+x}=C$

$P-C=\frac{P}{1+x}$

Interchanging numerators and denominators

$\frac{1}{P-C}=\frac{1+x}{P}$

$\frac{P}{P-C}=1+x$

$\frac{P}{P-C}-1=x$

$\frac{P}{P-C}-\frac{P-C}{P-C}=x$

$\boxed{\frac{C}{P-C}=x}$

With $P=1100$ and $C=100$

$x=\frac{100}{1100-100}=0.1=10\%$

Answer 2

I'm not sure I really understand the context, but I think what you're trying to do is solve the equation: \begin{equation} 1100(1 - \frac{1}{1 + p}) = 100 \end{equation} which yields $p = 0.10$.